/*
 * glMatrix.js - High performance matrix and vector operations for WebGL
 * version 0.9.5
 *
 * This is a MODIFIED copy of glMatrix.js for the purpose of integration
 * with the Wt C++ toolkit. This is therefore not the original software.
 *
 * Copyright (c) 2010 Brandon Jones
 *
 * This software is provided 'as-is', without any express or implied
 * warranty. In no event will the authors be held liable for any damages
 * arising from the use of this software.
 *
 * Permission is granted to anyone to use this software for any purpose,
 * including commercial applications, and to alter it and redistribute it
 * freely, subject to the following restrictions:
 *
 *    1. The origin of this software must not be misrepresented; you must not
 *    claim that you wrote the original software. If you use this software
 *    in a product, an acknowledgment in the product documentation would be
 *    appreciated but is not required.
 *
 *    2. Altered source versions must be plainly marked as such, and must not
 *    be misrepresented as being the original software.
 *
 *    3. This notice may not be removed or altered from any source
 *    distribution.
 */

WT_DECLARE_WT_MEMBER(
  2,
  JavaScriptObject,
  "glMatrix",
  (function() {
    let glMatrixArrayType;
    // Fallback for systems that don't support WebGL
    if (typeof Float32Array !== "undefined") {
      glMatrixArrayType = Float32Array;
    } else {
      glMatrixArrayType = Array;
    }

    /*
     * vec3 - 3 Dimensional Vector
     */
    const vec3 = {};

    /*
     * vec3.create
     * Creates a new instance of a vec3 using the default array type
     * Any javascript array containing at least 3 numeric elements can serve as a vec3
     *
     * Params:
     * vec - Optional, vec3 containing values to initialize with
     *
     * Returns:
     * New vec3
     */
    vec3.create = function(vec) {
      const dest = new glMatrixArrayType(3);

      if (vec) {
        dest[0] = vec[0];
        dest[1] = vec[1];
        dest[2] = vec[2];
      }

      return dest;
    };

    /*
     * vec3.set
     * Copies the values of one vec3 to another
     *
     * Params:
     * vec - vec3 containing values to copy
     * dest - vec3 receiving copied values
     *
     * Returns:
     * dest
     */
    vec3.set = function(vec, dest) {
      dest[0] = vec[0];
      dest[1] = vec[1];
      dest[2] = vec[2];

      return dest;
    };

    /*
     * vec3.add
     * Performs a vector addition
     *
     * Params:
     * vec - vec3, first operand
     * vec2 - vec3, second operand
     * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
     *
     * Returns:
     * dest if specified, vec otherwise
     */
    vec3.add = function(vec, vec2, dest) {
      if (!dest || vec === dest) {
        vec[0] += vec2[0];
        vec[1] += vec2[1];
        vec[2] += vec2[2];
        return vec;
      }

      dest[0] = vec[0] + vec2[0];
      dest[1] = vec[1] + vec2[1];
      dest[2] = vec[2] + vec2[2];
      return dest;
    };

    /*
     * vec3.subtract
     * Performs a vector subtraction
     *
     * Params:
     * vec - vec3, first operand
     * vec2 - vec3, second operand
     * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
     *
     * Returns:
     * dest if specified, vec otherwise
     */
    vec3.subtract = function(vec, vec2, dest) {
      if (!dest || vec === dest) {
        vec[0] -= vec2[0];
        vec[1] -= vec2[1];
        vec[2] -= vec2[2];
        return vec;
      }

      dest[0] = vec[0] - vec2[0];
      dest[1] = vec[1] - vec2[1];
      dest[2] = vec[2] - vec2[2];
      return dest;
    };

    /*
     * vec3.negate
     * Negates the components of a vec3
     *
     * Params:
     * vec - vec3 to negate
     * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
     *
     * Returns:
     * dest if specified, vec otherwise
     */
    vec3.negate = function(vec, dest) {
      if (!dest) {
        dest = vec;
      }

      dest[0] = -vec[0];
      dest[1] = -vec[1];
      dest[2] = -vec[2];
      return dest;
    };

    /*
     * vec3.scale
     * Multiplies the components of a vec3 by a scalar value
     *
     * Params:
     * vec - vec3 to scale
     * val - Numeric value to scale by
     * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
     *
     * Returns:
     * dest if specified, vec otherwise
     */
    vec3.scale = function(vec, val, dest) {
      if (!dest || vec === dest) {
        vec[0] *= val;
        vec[1] *= val;
        vec[2] *= val;
        return vec;
      }

      dest[0] = vec[0] * val;
      dest[1] = vec[1] * val;
      dest[2] = vec[2] * val;
      return dest;
    };

    /*
     * vec3.normalize
     * Generates a unit vector of the same direction as the provided vec3
     * If vector length is 0, returns [0, 0, 0]
     *
     * Params:
     * vec - vec3 to normalize
     * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
     *
     * Returns:
     * dest if specified, vec otherwise
     */
    vec3.normalize = function(vec, dest) {
      if (!dest) {
        dest = vec;
      }

      const x = vec[0], y = vec[1], z = vec[2];
      const len = Math.sqrt(x * x + y * y + z * z);

      if (!len) {
        dest[0] = 0;
        dest[1] = 0;
        dest[2] = 0;
        return dest;
      } else if (len === 1) {
        dest[0] = x;
        dest[1] = y;
        dest[2] = z;
        return dest;
      }

      const invLen = 1 / len;
      dest[0] = x * invLen;
      dest[1] = y * invLen;
      dest[2] = z * invLen;
      return dest;
    };

    /*
     * vec3.cross
     * Generates the cross product of two vec3s
     *
     * Params:
     * vec - vec3, first operand
     * vec2 - vec3, second operand
     * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
     *
     * Returns:
     * dest if specified, vec otherwise
     */
    vec3.cross = function(vec, vec2, dest) {
      if (!dest) {
        dest = vec;
      }

      const x = vec[0], y = vec[1], z = vec[2];
      const x2 = vec2[0], y2 = vec2[1], z2 = vec2[2];

      dest[0] = y * z2 - z * y2;
      dest[1] = z * x2 - x * z2;
      dest[2] = x * y2 - y * x2;
      return dest;
    };

    /*
     * vec3.length
     * Caclulates the length of a vec3
     *
     * Params:
     * vec - vec3 to calculate length of
     *
     * Returns:
     * Length of vec
     */
    vec3.length = function(vec) {
      const x = vec[0], y = vec[1], z = vec[2];
      return Math.sqrt(x * x + y * y + z * z);
    };

    /*
     * vec3.dot
     * Caclulates the dot product of two vec3s
     *
     * Params:
     * vec - vec3, first operand
     * vec2 - vec3, second operand
     *
     * Returns:
     * Dot product of vec and vec2
     */
    vec3.dot = function(vec, vec2) {
      return vec[0] * vec2[0] + vec[1] * vec2[1] + vec[2] * vec2[2];
    };

    /*
     * vec3.direction
     * Generates a unit vector pointing from one vector to another
     *
     * Params:
     * vec - origin vec3
     * vec2 - vec3 to point to
     * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
     *
     * Returns:
     * dest if specified, vec otherwise
     */
    vec3.direction = function(vec, vec2, dest) {
      if (!dest) {
        dest = vec;
      }

      const x = vec[0] - vec2[0];
      const y = vec[1] - vec2[1];
      const z = vec[2] - vec2[2];

      const len = Math.sqrt(x * x + y * y + z * z);
      if (!len) {
        dest[0] = 0;
        dest[1] = 0;
        dest[2] = 0;
        return dest;
      }

      const invLen = 1 / len;
      dest[0] = x * invLen;
      dest[1] = y * invLen;
      dest[2] = z * invLen;
      return dest;
    };

    /*
     * vec3.str
     * Returns a string representation of a vector
     *
     * Params:
     * vec - vec3 to represent as a string
     *
     * Returns:
     * string representation of vec
     */
    vec3.str = function(vec) {
      return "[" + vec[0] + ", " + vec[1] + ", " + vec[2] + "]";
    };

    /*
     * mat3 - 3x3 Matrix
     */
    const mat3 = {};

    /*
     * mat3.create
     * Creates a new instance of a mat3 using the default array type
     * Any javascript array containing at least 9 numeric elements can serve as a mat3
     *
     * Params:
     * mat - Optional, mat3 containing values to initialize with
     *
     * Returns:
     * New mat3
     */
    mat3.create = function(mat) {
      const dest = new glMatrixArrayType(9);

      if (mat) {
        dest[0] = mat[0];
        dest[1] = mat[1];
        dest[2] = mat[2];
        dest[3] = mat[3];
        dest[4] = mat[4];
        dest[5] = mat[5];
        dest[6] = mat[6];
        dest[7] = mat[7];
        dest[8] = mat[8];
        dest[9] = mat[9];
      }

      return dest;
    };

    /*
     * mat3.set
     * Copies the values of one mat3 to another
     *
     * Params:
     * mat - mat3 containing values to copy
     * dest - mat3 receiving copied values
     *
     * Returns:
     * dest
     */
    mat3.set = function(mat, dest) {
      dest[0] = mat[0];
      dest[1] = mat[1];
      dest[2] = mat[2];
      dest[3] = mat[3];
      dest[4] = mat[4];
      dest[5] = mat[5];
      dest[6] = mat[6];
      dest[7] = mat[7];
      dest[8] = mat[8];
      return dest;
    };

    /*
     * mat3.identity
     * Sets a mat3 to an identity matrix
     *
     * Params:
     * dest - mat3 to set
     *
     * Returns:
     * dest
     */
    mat3.identity = function(dest) {
      dest[0] = 1;
      dest[1] = 0;
      dest[2] = 0;
      dest[3] = 0;
      dest[4] = 1;
      dest[5] = 0;
      dest[6] = 0;
      dest[7] = 0;
      dest[8] = 1;
      return dest;
    };

    /*
     * mat3.toMat4
     * Copies the elements of a mat3 into the upper 3x3 elements of a mat4
     *
     * Params:
     * mat - mat3 containing values to copy
     * dest - Optional, mat4 receiving copied values
     *
     * Returns:
     * dest if specified, a new mat4 otherwise
     */
    mat3.toMat4 = function(mat, dest) {
      if (!dest) {
        dest = mat4.create();
      }

      dest[0] = mat[0];
      dest[1] = mat[1];
      dest[2] = mat[2];
      dest[3] = 0;

      dest[4] = mat[3];
      dest[5] = mat[4];
      dest[6] = mat[5];
      dest[7] = 0;

      dest[8] = mat[6];
      dest[9] = mat[7];
      dest[10] = mat[8];
      dest[11] = 0;

      dest[12] = 0;
      dest[13] = 0;
      dest[14] = 0;
      dest[15] = 1;

      return dest;
    };

    /*
     * mat3.str
     * Returns a string representation of a mat3
     *
     * Params:
     * mat - mat3 to represent as a string
     *
     * Returns:
     * string representation of mat
     */
    mat3.str = function(mat) {
      return "[" + mat[0] + ", " + mat[1] + ", " + mat[2] +
        ", " + mat[3] + ", " + mat[4] + ", " + mat[5] +
        ", " + mat[6] + ", " + mat[7] + ", " + mat[8] + "]";
    };

    /*
     * mat4 - 4x4 Matrix
     */
    const mat4 = {};

    /*
     * mat4.create
     * Creates a new instance of a mat4 using the default array type
     * Any javascript array containing at least 16 numeric elements can serve as a mat4
     *
     * Params:
     * mat - Optional, mat4 containing values to initialize with
     *
     * Returns:
     * New mat4
     */
    mat4.create = function(mat) {
      const dest = new glMatrixArrayType(16);

      if (mat) {
        dest[0] = mat[0];
        dest[1] = mat[1];
        dest[2] = mat[2];
        dest[3] = mat[3];
        dest[4] = mat[4];
        dest[5] = mat[5];
        dest[6] = mat[6];
        dest[7] = mat[7];
        dest[8] = mat[8];
        dest[9] = mat[9];
        dest[10] = mat[10];
        dest[11] = mat[11];
        dest[12] = mat[12];
        dest[13] = mat[13];
        dest[14] = mat[14];
        dest[15] = mat[15];
      }

      return dest;
    };

    /*
     * mat4.set
     * Copies the values of one mat4 to another
     *
     * Params:
     * mat - mat4 containing values to copy
     * dest - mat4 receiving copied values
     *
     * Returns:
     * dest
     */
    mat4.set = function(mat, dest) {
      dest[0] = mat[0];
      dest[1] = mat[1];
      dest[2] = mat[2];
      dest[3] = mat[3];
      dest[4] = mat[4];
      dest[5] = mat[5];
      dest[6] = mat[6];
      dest[7] = mat[7];
      dest[8] = mat[8];
      dest[9] = mat[9];
      dest[10] = mat[10];
      dest[11] = mat[11];
      dest[12] = mat[12];
      dest[13] = mat[13];
      dest[14] = mat[14];
      dest[15] = mat[15];
      return dest;
    };

    /*
     * mat4.identity
     * Sets a mat4 to an identity matrix
     *
     * Params:
     * dest - mat4 to set
     *
     * Returns:
     * dest
     */
    mat4.identity = function(dest) {
      dest[0] = 1;
      dest[1] = 0;
      dest[2] = 0;
      dest[3] = 0;
      dest[4] = 0;
      dest[5] = 1;
      dest[6] = 0;
      dest[7] = 0;
      dest[8] = 0;
      dest[9] = 0;
      dest[10] = 1;
      dest[11] = 0;
      dest[12] = 0;
      dest[13] = 0;
      dest[14] = 0;
      dest[15] = 1;
      return dest;
    };

    /*
     * mat4.transpose
     * Transposes a mat4 (flips the values over the diagonal)
     *
     * Params:
     * mat - mat4 to transpose
     * dest - Optional, mat4 receiving transposed values. If not specified result is written to mat
     *
     * Returns:
     * dest is specified, mat otherwise
     */
    mat4.transpose = function(mat, dest) {
      // If we are transposing ourselves we can skip a few steps but have to cache some values
      if (!dest || mat === dest) {
        const a01 = mat[1], a02 = mat[2], a03 = mat[3];
        const a12 = mat[6], a13 = mat[7];
        const a23 = mat[11];

        mat[1] = mat[4];
        mat[2] = mat[8];
        mat[3] = mat[12];
        mat[4] = a01;
        mat[6] = mat[9];
        mat[7] = mat[13];
        mat[8] = a02;
        mat[9] = a12;
        mat[11] = mat[14];
        mat[12] = a03;
        mat[13] = a13;
        mat[14] = a23;
        return mat;
      }

      dest[0] = mat[0];
      dest[1] = mat[4];
      dest[2] = mat[8];
      dest[3] = mat[12];
      dest[4] = mat[1];
      dest[5] = mat[5];
      dest[6] = mat[9];
      dest[7] = mat[13];
      dest[8] = mat[2];
      dest[9] = mat[6];
      dest[10] = mat[10];
      dest[11] = mat[14];
      dest[12] = mat[3];
      dest[13] = mat[7];
      dest[14] = mat[11];
      dest[15] = mat[15];
      return dest;
    };

    /*
     * mat4.determinant
     * Calculates the determinant of a mat4
     *
     * Params:
     * mat - mat4 to calculate determinant of
     *
     * Returns:
     * determinant of mat
     */
    mat4.determinant = function(mat) {
      // Cache the matrix values (makes for huge speed increases!)
      const a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
      const a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
      const a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
      const a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15];

      return a30 * a21 * a12 * a03 - a20 * a31 * a12 * a03 - a30 * a11 * a22 * a03 + a10 * a31 * a22 * a03 +
        a20 * a11 * a32 * a03 - a10 * a21 * a32 * a03 - a30 * a21 * a02 * a13 + a20 * a31 * a02 * a13 +
        a30 * a01 * a22 * a13 - a00 * a31 * a22 * a13 - a20 * a01 * a32 * a13 + a00 * a21 * a32 * a13 +
        a30 * a11 * a02 * a23 - a10 * a31 * a02 * a23 - a30 * a01 * a12 * a23 + a00 * a31 * a12 * a23 +
        a10 * a01 * a32 * a23 - a00 * a11 * a32 * a23 - a20 * a11 * a02 * a33 + a10 * a21 * a02 * a33 +
        a20 * a01 * a12 * a33 - a00 * a21 * a12 * a33 - a10 * a01 * a22 * a33 + a00 * a11 * a22 * a33;
    };

    /*
     * mat4.inverse
     * Calculates the inverse matrix of a mat4
     *
     * Params:
     * mat - mat4 to calculate inverse of
     * dest - Optional, mat4 receiving inverse matrix. If not specified result is written to mat
     *
     * Returns:
     * dest is specified, mat otherwise
     */
    mat4.inverse = function(mat, dest) {
      if (!dest) {
        dest = mat;
      }

      // Cache the matrix values (makes for huge speed increases!)
      const a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
      const a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
      const a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
      const a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15];

      const b00 = a00 * a11 - a01 * a10;
      const b01 = a00 * a12 - a02 * a10;
      const b02 = a00 * a13 - a03 * a10;
      const b03 = a01 * a12 - a02 * a11;
      const b04 = a01 * a13 - a03 * a11;
      const b05 = a02 * a13 - a03 * a12;
      const b06 = a20 * a31 - a21 * a30;
      const b07 = a20 * a32 - a22 * a30;
      const b08 = a20 * a33 - a23 * a30;
      const b09 = a21 * a32 - a22 * a31;
      const b10 = a21 * a33 - a23 * a31;
      const b11 = a22 * a33 - a23 * a32;

      // Calculate the determinant (inlined to avoid double-caching)
      const invDet = 1 / (b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06);

      dest[0] = (a11 * b11 - a12 * b10 + a13 * b09) * invDet;
      dest[1] = (-a01 * b11 + a02 * b10 - a03 * b09) * invDet;
      dest[2] = (a31 * b05 - a32 * b04 + a33 * b03) * invDet;
      dest[3] = (-a21 * b05 + a22 * b04 - a23 * b03) * invDet;
      dest[4] = (-a10 * b11 + a12 * b08 - a13 * b07) * invDet;
      dest[5] = (a00 * b11 - a02 * b08 + a03 * b07) * invDet;
      dest[6] = (-a30 * b05 + a32 * b02 - a33 * b01) * invDet;
      dest[7] = (a20 * b05 - a22 * b02 + a23 * b01) * invDet;
      dest[8] = (a10 * b10 - a11 * b08 + a13 * b06) * invDet;
      dest[9] = (-a00 * b10 + a01 * b08 - a03 * b06) * invDet;
      dest[10] = (a30 * b04 - a31 * b02 + a33 * b00) * invDet;
      dest[11] = (-a20 * b04 + a21 * b02 - a23 * b00) * invDet;
      dest[12] = (-a10 * b09 + a11 * b07 - a12 * b06) * invDet;
      dest[13] = (a00 * b09 - a01 * b07 + a02 * b06) * invDet;
      dest[14] = (-a30 * b03 + a31 * b01 - a32 * b00) * invDet;
      dest[15] = (a20 * b03 - a21 * b01 + a22 * b00) * invDet;

      return dest;
    };

    /*
     * mat4.toRotationMat
     * Copies the upper 3x3 elements of a mat4 into another mat4
     *
     * Params:
     * mat - mat4 containing values to copy
     * dest - Optional, mat4 receiving copied values
     *
     * Returns:
     * dest is specified, a new mat4 otherwise
     */
    mat4.toRotationMat = function(mat, dest) {
      if (!dest) {
        dest = mat4.create();
      }

      dest[0] = mat[0];
      dest[1] = mat[1];
      dest[2] = mat[2];
      dest[3] = mat[3];
      dest[4] = mat[4];
      dest[5] = mat[5];
      dest[6] = mat[6];
      dest[7] = mat[7];
      dest[8] = mat[8];
      dest[9] = mat[9];
      dest[10] = mat[10];
      dest[11] = mat[11];
      dest[12] = 0;
      dest[13] = 0;
      dest[14] = 0;
      dest[15] = 1;

      return dest;
    };

    /*
     * mat4.toMat3
     * Copies the upper 3x3 elements of a mat4 into a mat3
     *
     * Params:
     * mat - mat4 containing values to copy
     * dest - Optional, mat3 receiving copied values
     *
     * Returns:
     * dest is specified, a new mat3 otherwise
     */
    mat4.toMat3 = function(mat, dest) {
      if (!dest) {
        dest = mat3.create();
      }

      dest[0] = mat[0];
      dest[1] = mat[1];
      dest[2] = mat[2];
      dest[3] = mat[4];
      dest[4] = mat[5];
      dest[5] = mat[6];
      dest[6] = mat[8];
      dest[7] = mat[9];
      dest[8] = mat[10];

      return dest;
    };

    /*
     * mat4.toInverseMat3
     * Calculates the inverse of the upper 3x3 elements of a mat4 and copies the result into a mat3
     * The resulting matrix is useful for calculating transformed normals
     *
     * Params:
     * mat - mat4 containing values to invert and copy
     * dest - Optional, mat3 receiving values
     *
     * Returns:
     * dest is specified, a new mat3 otherwise
     */
    mat4.toInverseMat3 = function(mat, dest) {
      // Cache the matrix values (makes for huge speed increases!)
      const a00 = mat[0], a01 = mat[1], a02 = mat[2];
      const a10 = mat[4], a11 = mat[5], a12 = mat[6];
      const a20 = mat[8], a21 = mat[9], a22 = mat[10];

      const b01 = a22 * a11 - a12 * a21;
      const b11 = -a22 * a10 + a12 * a20;
      const b21 = a21 * a10 - a11 * a20;

      const d = a00 * b01 + a01 * b11 + a02 * b21;
      if (!d) {
        return null;
      }
      const id = 1 / d;

      if (!dest) {
        dest = mat3.create();
      }

      dest[0] = b01 * id;
      dest[1] = (-a22 * a01 + a02 * a21) * id;
      dest[2] = (a12 * a01 - a02 * a11) * id;
      dest[3] = b11 * id;
      dest[4] = (a22 * a00 - a02 * a20) * id;
      dest[5] = (-a12 * a00 + a02 * a10) * id;
      dest[6] = b21 * id;
      dest[7] = (-a21 * a00 + a01 * a20) * id;
      dest[8] = (a11 * a00 - a01 * a10) * id;

      return dest;
    };

    /*
     * mat4.multiply
     * Performs a matrix multiplication
     *
     * Params:
     * mat - mat4, first operand
     * mat2 - mat4, second operand
     * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
     *
     * Returns:
     * dest if specified, mat otherwise
     */
    mat4.multiply = function(mat, mat2, dest) {
      if (!dest) {
        dest = mat;
      }

      // Cache the matrix values (makes for huge speed increases!)
      const a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
      const a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
      const a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
      const a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15];

      const b00 = mat2[0], b01 = mat2[1], b02 = mat2[2], b03 = mat2[3];
      const b10 = mat2[4], b11 = mat2[5], b12 = mat2[6], b13 = mat2[7];
      const b20 = mat2[8], b21 = mat2[9], b22 = mat2[10], b23 = mat2[11];
      const b30 = mat2[12], b31 = mat2[13], b32 = mat2[14], b33 = mat2[15];

      dest[0] = b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30;
      dest[1] = b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31;
      dest[2] = b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32;
      dest[3] = b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33;
      dest[4] = b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30;
      dest[5] = b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31;
      dest[6] = b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32;
      dest[7] = b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33;
      dest[8] = b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30;
      dest[9] = b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31;
      dest[10] = b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32;
      dest[11] = b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33;
      dest[12] = b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30;
      dest[13] = b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31;
      dest[14] = b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32;
      dest[15] = b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33;

      return dest;
    };

    /*
     * mat4.multiplyVec3
     * Transforms a vec3 with the given matrix
     * 4th vector component is implicitly '1'
     *
     * Params:
     * mat - mat4 to transform the vector with
     * vec - vec3 to transform
     * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
     *
     * Returns:
     * dest if specified, vec otherwise
     */
    mat4.multiplyVec3 = function(mat, vec, dest) {
      if (!dest) {
        dest = vec;
      }

      const x = vec[0], y = vec[1], z = vec[2];

      dest[0] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12];
      dest[1] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13];
      dest[2] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14];

      return dest;
    };

    /*
     * mat4.multiplyVec4
     * Transforms a vec4 with the given matrix
     *
     * Params:
     * mat - mat4 to transform the vector with
     * vec - vec4 to transform
     * dest - Optional, vec4 receiving operation result. If not specified result is written to vec
     *
     * Returns:
     * dest if specified, vec otherwise
     */
    mat4.multiplyVec4 = function(mat, vec, dest) {
      if (!dest) {
        dest = vec;
      }

      const x = vec[0], y = vec[1], z = vec[2], w = vec[3];

      dest[0] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12] * w;
      dest[1] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13] * w;
      dest[2] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14] * w;
      dest[3] = mat[3] * x + mat[7] * y + mat[11] * z + mat[15] * w;

      return dest;
    };

    /*
     * mat4.translate
     * Translates a matrix by the given vector
     *
     * Params:
     * mat - mat4 to translate
     * vec - vec3 specifying the translation
     * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
     *
     * Returns:
     * dest if specified, mat otherwise
     */
    mat4.translate = function(mat, vec, dest) {
      const x = vec[0], y = vec[1], z = vec[2];

      if (!dest || mat === dest) {
        mat[12] = mat[0] * x + mat[4] * y + mat[8] * z + mat[12];
        mat[13] = mat[1] * x + mat[5] * y + mat[9] * z + mat[13];
        mat[14] = mat[2] * x + mat[6] * y + mat[10] * z + mat[14];
        mat[15] = mat[3] * x + mat[7] * y + mat[11] * z + mat[15];
        return mat;
      }

      const a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
      const a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
      const a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];

      dest[0] = a00;
      dest[1] = a01;
      dest[2] = a02;
      dest[3] = a03;
      dest[4] = a10;
      dest[5] = a11;
      dest[6] = a12;
      dest[7] = a13;
      dest[8] = a20;
      dest[9] = a21;
      dest[10] = a22;
      dest[11] = a23;

      dest[12] = a00 * x + a10 * y + a20 * z + mat[12];
      dest[13] = a01 * x + a11 * y + a21 * z + mat[13];
      dest[14] = a02 * x + a12 * y + a22 * z + mat[14];
      dest[15] = a03 * x + a13 * y + a23 * z + mat[15];
      return dest;
    };

    /*
     * mat4.scale
     * Scales a matrix by the given vector
     *
     * Params:
     * mat - mat4 to scale
     * vec - vec3 specifying the scale for each axis
     * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
     *
     * Returns:
     * dest if specified, mat otherwise
     */
    mat4.scale = function(mat, vec, dest) {
      const x = vec[0], y = vec[1], z = vec[2];

      if (!dest || mat === dest) {
        mat[0] *= x;
        mat[1] *= x;
        mat[2] *= x;
        mat[3] *= x;
        mat[4] *= y;
        mat[5] *= y;
        mat[6] *= y;
        mat[7] *= y;
        mat[8] *= z;
        mat[9] *= z;
        mat[10] *= z;
        mat[11] *= z;
        return mat;
      }

      dest[0] = mat[0] * x;
      dest[1] = mat[1] * x;
      dest[2] = mat[2] * x;
      dest[3] = mat[3] * x;
      dest[4] = mat[4] * y;
      dest[5] = mat[5] * y;
      dest[6] = mat[6] * y;
      dest[7] = mat[7] * y;
      dest[8] = mat[8] * z;
      dest[9] = mat[9] * z;
      dest[10] = mat[10] * z;
      dest[11] = mat[11] * z;
      dest[12] = mat[12];
      dest[13] = mat[13];
      dest[14] = mat[14];
      dest[15] = mat[15];
      return dest;
    };

    /*
     * mat4.rotate
     * Rotates a matrix by the given angle around the specified axis
     * If rotating around a primary axis (X,Y,Z) one of the specialized rotation
     * functions should be used instead for performance
     *
     * Params:
     * mat - mat4 to rotate
     * angle - angle (in radians) to rotate
     * axis - vec3 representing the axis to rotate around
     * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
     *
     * Returns:
     * dest if specified, mat otherwise
     */
    mat4.rotate = function(mat, angle, axis, dest) {
      let x = axis[0], y = axis[1], z = axis[2];
      const len = Math.sqrt(x * x + y * y + z * z);
      if (!len) {
        return null;
      }
      if (len !== 1) {
        const invLen = 1 / len;
        x *= invLen;
        y *= invLen;
        z *= invLen;
      }

      const s = Math.sin(angle);
      const c = Math.cos(angle);
      const t = 1 - c;

      // Cache the matrix values (makes for huge speed increases!)
      const a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
      const a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
      const a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];

      // Construct the elements of the rotation matrix
      const b00 = x * x * t + c, b01 = y * x * t + z * s, b02 = z * x * t - y * s;
      const b10 = x * y * t - z * s, b11 = y * y * t + c, b12 = z * y * t + x * s;
      const b20 = x * z * t + y * s, b21 = y * z * t - x * s, b22 = z * z * t + c;

      if (!dest) {
        dest = mat;
      } else if (mat !== dest) { // If the source and destination differ, copy the unchanged last row
        dest[12] = mat[12];
        dest[13] = mat[13];
        dest[14] = mat[14];
        dest[15] = mat[15];
      }

      // Perform rotation-specific matrix multiplication
      dest[0] = a00 * b00 + a10 * b01 + a20 * b02;
      dest[1] = a01 * b00 + a11 * b01 + a21 * b02;
      dest[2] = a02 * b00 + a12 * b01 + a22 * b02;
      dest[3] = a03 * b00 + a13 * b01 + a23 * b02;

      dest[4] = a00 * b10 + a10 * b11 + a20 * b12;
      dest[5] = a01 * b10 + a11 * b11 + a21 * b12;
      dest[6] = a02 * b10 + a12 * b11 + a22 * b12;
      dest[7] = a03 * b10 + a13 * b11 + a23 * b12;

      dest[8] = a00 * b20 + a10 * b21 + a20 * b22;
      dest[9] = a01 * b20 + a11 * b21 + a21 * b22;
      dest[10] = a02 * b20 + a12 * b21 + a22 * b22;
      dest[11] = a03 * b20 + a13 * b21 + a23 * b22;
      return dest;
    };

    /*
     * mat4.rotateX
     * Rotates a matrix by the given angle around the X axis
     *
     * Params:
     * mat - mat4 to rotate
     * angle - angle (in radians) to rotate
     * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
     *
     * Returns:
     * dest if specified, mat otherwise
     */
    mat4.rotateX = function(mat, angle, dest) {
      const s = Math.sin(angle);
      const c = Math.cos(angle);

      // Cache the matrix values (makes for huge speed increases!)
      const a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
      const a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];

      if (!dest) {
        dest = mat;
      } else if (mat !== dest) { // If the source and destination differ, copy the unchanged rows
        dest[0] = mat[0];
        dest[1] = mat[1];
        dest[2] = mat[2];
        dest[3] = mat[3];

        dest[12] = mat[12];
        dest[13] = mat[13];
        dest[14] = mat[14];
        dest[15] = mat[15];
      }

      // Perform axis-specific matrix multiplication
      dest[4] = a10 * c + a20 * s;
      dest[5] = a11 * c + a21 * s;
      dest[6] = a12 * c + a22 * s;
      dest[7] = a13 * c + a23 * s;

      dest[8] = a10 * -s + a20 * c;
      dest[9] = a11 * -s + a21 * c;
      dest[10] = a12 * -s + a22 * c;
      dest[11] = a13 * -s + a23 * c;
      return dest;
    };

    /*
     * mat4.rotateY
     * Rotates a matrix by the given angle around the Y axis
     *
     * Params:
     * mat - mat4 to rotate
     * angle - angle (in radians) to rotate
     * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
     *
     * Returns:
     * dest if specified, mat otherwise
     */
    mat4.rotateY = function(mat, angle, dest) {
      const s = Math.sin(angle);
      const c = Math.cos(angle);

      // Cache the matrix values (makes for huge speed increases!)
      const a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
      const a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];

      if (!dest) {
        dest = mat;
      } else if (mat !== dest) { // If the source and destination differ, copy the unchanged rows
        dest[4] = mat[4];
        dest[5] = mat[5];
        dest[6] = mat[6];
        dest[7] = mat[7];

        dest[12] = mat[12];
        dest[13] = mat[13];
        dest[14] = mat[14];
        dest[15] = mat[15];
      }

      // Perform axis-specific matrix multiplication
      dest[0] = a00 * c + a20 * -s;
      dest[1] = a01 * c + a21 * -s;
      dest[2] = a02 * c + a22 * -s;
      dest[3] = a03 * c + a23 * -s;

      dest[8] = a00 * s + a20 * c;
      dest[9] = a01 * s + a21 * c;
      dest[10] = a02 * s + a22 * c;
      dest[11] = a03 * s + a23 * c;
      return dest;
    };

    /*
     * mat4.rotateZ
     * Rotates a matrix by the given angle around the Z axis
     *
     * Params:
     * mat - mat4 to rotate
     * angle - angle (in radians) to rotate
     * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
     *
     * Returns:
     * dest if specified, mat otherwise
     */
    mat4.rotateZ = function(mat, angle, dest) {
      const s = Math.sin(angle);
      const c = Math.cos(angle);

      // Cache the matrix values (makes for huge speed increases!)
      const a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
      const a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];

      if (!dest) {
        dest = mat;
      } else if (mat !== dest) { // If the source and destination differ, copy the unchanged last row
        dest[8] = mat[8];
        dest[9] = mat[9];
        dest[10] = mat[10];
        dest[11] = mat[11];

        dest[12] = mat[12];
        dest[13] = mat[13];
        dest[14] = mat[14];
        dest[15] = mat[15];
      }

      // Perform axis-specific matrix multiplication
      dest[0] = a00 * c + a10 * s;
      dest[1] = a01 * c + a11 * s;
      dest[2] = a02 * c + a12 * s;
      dest[3] = a03 * c + a13 * s;

      dest[4] = a00 * -s + a10 * c;
      dest[5] = a01 * -s + a11 * c;
      dest[6] = a02 * -s + a12 * c;
      dest[7] = a03 * -s + a13 * c;

      return dest;
    };

    /*
     * mat4.frustum
     * Generates a frustum matrix with the given bounds
     *
     * Params:
     * left, right - scalar, left and right bounds of the frustum
     * bottom, top - scalar, bottom and top bounds of the frustum
     * near, far - scalar, near and far bounds of the frustum
     * dest - Optional, mat4 frustum matrix will be written into
     *
     * Returns:
     * dest if specified, a new mat4 otherwise
     */
    mat4.frustum = function(left, right, bottom, top, near, far, dest) {
      if (!dest) {
        dest = mat4.create();
      }
      const rl = (right - left);
      const tb = (top - bottom);
      const fn = (far - near);
      dest[0] = (near * 2) / rl;
      dest[1] = 0;
      dest[2] = 0;
      dest[3] = 0;
      dest[4] = 0;
      dest[5] = (near * 2) / tb;
      dest[6] = 0;
      dest[7] = 0;
      dest[8] = (right + left) / rl;
      dest[9] = (top + bottom) / tb;
      dest[10] = -(far + near) / fn;
      dest[11] = -1;
      dest[12] = 0;
      dest[13] = 0;
      dest[14] = -(far * near * 2) / fn;
      dest[15] = 0;
      return dest;
    };

    /*
     * mat4.perspective
     * Generates a perspective projection matrix with the given bounds
     *
     * Params:
     * fovy - scalar, vertical field of view
     * aspect - scalar, aspect ratio. typically viewport width/height
     * near, far - scalar, near and far bounds of the frustum
     * dest - Optional, mat4 frustum matrix will be written into
     *
     * Returns:
     * dest if specified, a new mat4 otherwise
     */
    mat4.perspective = function(fovy, aspect, near, far, dest) {
      const top = near * Math.tan(fovy * Math.PI / 360.0);
      const right = top * aspect;
      return mat4.frustum(-right, right, -top, top, near, far, dest);
    };

    /*
     * mat4.ortho
     * Generates a orthogonal projection matrix with the given bounds
     *
     * Params:
     * left, right - scalar, left and right bounds of the frustum
     * bottom, top - scalar, bottom and top bounds of the frustum
     * near, far - scalar, near and far bounds of the frustum
     * dest - Optional, mat4 frustum matrix will be written into
     *
     * Returns:
     * dest if specified, a new mat4 otherwise
     */
    mat4.ortho = function(left, right, bottom, top, near, far, dest) {
      if (!dest) {
        dest = mat4.create();
      }
      const rl = (right - left);
      const tb = (top - bottom);
      const fn = (far - near);
      dest[0] = 2 / rl;
      dest[1] = 0;
      dest[2] = 0;
      dest[3] = 0;
      dest[4] = 0;
      dest[5] = 2 / tb;
      dest[6] = 0;
      dest[7] = 0;
      dest[8] = 0;
      dest[9] = 0;
      dest[10] = -2 / fn;
      dest[11] = 0;
      dest[12] = -(left + right) / rl;
      dest[13] = -(top + bottom) / tb;
      dest[14] = -(far + near) / fn;
      dest[15] = 1;
      return dest;
    };

    /*
 * mat4.ortho
 * Generates a look-at matrix with the given eye position, focal point, and up axis
 *
 * Params:
 * eye - vec3, position of the viewer
 * center - vec3, point the viewer is looking at
 * up - vec3 pointing "up"
 * dest - Optional, mat4 frustum matrix will be written into
 *
 * Returns:
 * dest if specified, a new mat4 otherwise
 */
    mat4.lookAt = function(eye, center, up, dest) {
      if (!dest) {
        dest = mat4.create();
      }

      const eyex = eye[0],
        eyey = eye[1],
        eyez = eye[2],
        upx = up[0],
        upy = up[1],
        upz = up[2],
        centerx = center[0],
        centery = center[1],
        centerz = center[2];

      if (eyex === centerx && eyey === centery && eyez === centerz) {
        return mat4.identity(dest);
      }

      let z0, z1, z2, x0, x1, x2, y0, y1, y2, len;

      // vec3.direction(eye, center, z);
      z0 = eyex - center[0];
      z1 = eyey - center[1];
      z2 = eyez - center[2];

      // normalize (no check needed for 0 because of early return)
      len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
      z0 *= len;
      z1 *= len;
      z2 *= len;

      // vec3.normalize(vec3.cross(up, z, x));
      x0 = upy * z2 - upz * z1;
      x1 = upz * z0 - upx * z2;
      x2 = upx * z1 - upy * z0;
      len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2);
      if (!len) {
        x0 = 0;
        x1 = 0;
        x2 = 0;
      } else {
        len = 1 / len;
        x0 *= len;
        x1 *= len;
        x2 *= len;
      }

      // vec3.normalize(vec3.cross(z, x, y));
      y0 = z1 * x2 - z2 * x1;
      y1 = z2 * x0 - z0 * x2;
      y2 = z0 * x1 - z1 * x0;

      len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2);
      if (!len) {
        y0 = 0;
        y1 = 0;
        y2 = 0;
      } else {
        len = 1 / len;
        y0 *= len;
        y1 *= len;
        y2 *= len;
      }

      dest[0] = x0;
      dest[1] = y0;
      dest[2] = z0;
      dest[3] = 0;
      dest[4] = x1;
      dest[5] = y1;
      dest[6] = z1;
      dest[7] = 0;
      dest[8] = x2;
      dest[9] = y2;
      dest[10] = z2;
      dest[11] = 0;
      dest[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
      dest[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
      dest[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
      dest[15] = 1;

      return dest;
    };

    /*
     * mat4.str
     * Returns a string representation of a mat4
     *
     * Params:
     * mat - mat4 to represent as a string
     *
     * Returns:
     * string representation of mat
     */
    mat4.str = function(mat) {
      return "[" + mat[0] + ", " + mat[1] + ", " + mat[2] + ", " + mat[3] +
        ", " + mat[4] + ", " + mat[5] + ", " + mat[6] + ", " + mat[7] +
        ", " + mat[8] + ", " + mat[9] + ", " + mat[10] + ", " + mat[11] +
        ", " + mat[12] + ", " + mat[13] + ", " + mat[14] + ", " + mat[15] + "]";
    };

    /*
     * quat4 - Quaternions
     */
    const quat4 = {};

    /*
     * quat4.create
     * Creates a new instance of a quat4 using the default array type
     * Any javascript array containing at least 4 numeric elements can serve as a quat4
     *
     * Params:
     * quat - Optional, quat4 containing values to initialize with
     *
     * Returns:
     * New quat4
     */
    quat4.create = function(quat) {
      const dest = new glMatrixArrayType(4);

      if (quat) {
        dest[0] = quat[0];
        dest[1] = quat[1];
        dest[2] = quat[2];
        dest[3] = quat[3];
      }

      return dest;
    };

    /*
     * quat4.set
     * Copies the values of one quat4 to another
     *
     * Params:
     * quat - quat4 containing values to copy
     * dest - quat4 receiving copied values
     *
     * Returns:
     * dest
     */
    quat4.set = function(quat, dest) {
      dest[0] = quat[0];
      dest[1] = quat[1];
      dest[2] = quat[2];
      dest[3] = quat[3];

      return dest;
    };

    /*
     * quat4.calculateW
     * Calculates the W component of a quat4 from the X, Y, and Z components.
     * Assumes that quaternion is 1 unit in length.
     * Any existing W component will be ignored.
     *
     * Params:
     * quat - quat4 to calculate W component of
     * dest - Optional, quat4 receiving calculated values. If not specified result is written to quat
     *
     * Returns:
     * dest if specified, quat otherwise
     */
    quat4.calculateW = function(quat, dest) {
      const x = quat[0], y = quat[1], z = quat[2];

      if (!dest || quat === dest) {
        quat[3] = -Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z));
        return quat;
      }
      dest[0] = x;
      dest[1] = y;
      dest[2] = z;
      dest[3] = -Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z));
      return dest;
    };

    /*
     * quat4.inverse
     * Calculates the inverse of a quat4
     *
     * Params:
     * quat - quat4 to calculate inverse of
     * dest - Optional, quat4 receiving inverse values. If not specified result is written to quat
     *
     * Returns:
     * dest if specified, quat otherwise
     */
    quat4.inverse = function(quat, dest) {
      if (!dest || quat === dest) {
        quat[0] *= 1;
        quat[1] *= 1;
        quat[2] *= 1;
        return quat;
      }
      dest[0] = -quat[0];
      dest[1] = -quat[1];
      dest[2] = -quat[2];
      dest[3] = quat[3];
      return dest;
    };

    /*
     * quat4.length
     * Calculates the length of a quat4
     *
     * Params:
     * quat - quat4 to calculate length of
     *
     * Returns:
     * Length of quat
     */
    quat4.length = function(quat) {
      const x = quat[0], y = quat[1], z = quat[2], w = quat[3];
      return Math.sqrt(x * x + y * y + z * z + w * w);
    };

    /*
     * quat4.normalize
     * Generates a unit quaternion of the same direction as the provided quat4
     * If quaternion length is 0, returns [0, 0, 0, 0]
     *
     * Params:
     * quat - quat4 to normalize
     * dest - Optional, quat4 receiving operation result. If not specified result is written to quat
     *
     * Returns:
     * dest if specified, quat otherwise
     */
    quat4.normalize = function(quat, dest) {
      if (!dest) {
        dest = quat;
      }

      const x = quat[0], y = quat[1], z = quat[2], w = quat[3];
      const len = Math.sqrt(x * x + y * y + z * z + w * w);
      if (len === 0) {
        dest[0] = 0;
        dest[1] = 0;
        dest[2] = 0;
        dest[3] = 0;
        return dest;
      }
      const invLen = 1 / len;
      dest[0] = x * invLen;
      dest[1] = y * invLen;
      dest[2] = z * invLen;
      dest[3] = w * invLen;

      return dest;
    };

    /*
     * quat4.multiply
     * Performs a quaternion multiplication
     *
     * Params:
     * quat - quat4, first operand
     * quat2 - quat4, second operand
     * dest - Optional, quat4 receiving operation result. If not specified result is written to quat
     *
     * Returns:
     * dest if specified, quat otherwise
     */
    quat4.multiply = function(quat, quat2, dest) {
      if (!dest) {
        dest = quat;
      }

      const qax = quat[0], qay = quat[1], qaz = quat[2], qaw = quat[3];
      const qbx = quat2[0], qby = quat2[1], qbz = quat2[2], qbw = quat2[3];

      dest[0] = qax * qbw + qaw * qbx + qay * qbz - qaz * qby;
      dest[1] = qay * qbw + qaw * qby + qaz * qbx - qax * qbz;
      dest[2] = qaz * qbw + qaw * qbz + qax * qby - qay * qbx;
      dest[3] = qaw * qbw - qax * qbx - qay * qby - qaz * qbz;

      return dest;
    };

    /*
     * quat4.multiplyVec3
     * Transforms a vec3 with the given quaternion
     *
     * Params:
     * quat - quat4 to transform the vector with
     * vec - vec3 to transform
     * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
     *
     * Returns:
     * dest if specified, vec otherwise
     */
    quat4.multiplyVec3 = function(quat, vec, dest) {
      if (!dest) {
        dest = vec;
      }

      const x = vec[0], y = vec[1], z = vec[2];
      const qx = quat[0], qy = quat[1], qz = quat[2], qw = quat[3];

      // calculate quat * vec
      const ix = qw * x + qy * z - qz * y;
      const iy = qw * y + qz * x - qx * z;
      const iz = qw * z + qx * y - qy * x;
      const iw = -qx * x - qy * y - qz * z;

      // calculate result * inverse quat
      dest[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy;
      dest[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz;
      dest[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx;

      return dest;
    };

    /*
     * quat4.toMat3
     * Calculates a 3x3 matrix from the given quat4
     *
     * Params:
     * quat - quat4 to create matrix from
     * dest - Optional, mat3 receiving operation result
     *
     * Returns:
     * dest if specified, a new mat3 otherwise
     */
    quat4.toMat3 = function(quat, dest) {
      if (!dest) {
        dest = mat3.create();
      }

      const x = quat[0], y = quat[1], z = quat[2], w = quat[3];

      const x2 = x + x;
      const y2 = y + y;
      const z2 = z + z;

      const xx = x * x2;
      const xy = x * y2;
      const xz = x * z2;

      const yy = y * y2;
      const yz = y * z2;
      const zz = z * z2;

      const wx = w * x2;
      const wy = w * y2;
      const wz = w * z2;

      dest[0] = 1 - (yy + zz);
      dest[1] = xy - wz;
      dest[2] = xz + wy;

      dest[3] = xy + wz;
      dest[4] = 1 - (xx + zz);
      dest[5] = yz - wx;

      dest[6] = xz - wy;
      dest[7] = yz + wx;
      dest[8] = 1 - (xx + yy);

      return dest;
    };

    /*
     * quat4.toMat4
     * Calculates a 4x4 matrix from the given quat4
     *
     * Params:
     * quat - quat4 to create matrix from
     * dest - Optional, mat4 receiving operation result
     *
     * Returns:
     * dest if specified, a new mat4 otherwise
     */
    quat4.toMat4 = function(quat, dest) {
      if (!dest) {
        dest = mat4.create();
      }

      const x = quat[0], y = quat[1], z = quat[2], w = quat[3];

      const x2 = x + x;
      const y2 = y + y;
      const z2 = z + z;

      const xx = x * x2;
      const xy = x * y2;
      const xz = x * z2;

      const yy = y * y2;
      const yz = y * z2;
      const zz = z * z2;

      const wx = w * x2;
      const wy = w * y2;
      const wz = w * z2;

      dest[0] = 1 - (yy + zz);
      dest[1] = xy - wz;
      dest[2] = xz + wy;
      dest[3] = 0;

      dest[4] = xy + wz;
      dest[5] = 1 - (xx + zz);
      dest[6] = yz - wx;
      dest[7] = 0;

      dest[8] = xz - wy;
      dest[9] = yz + wx;
      dest[10] = 1 - (xx + yy);
      dest[11] = 0;

      dest[12] = 0;
      dest[13] = 0;
      dest[14] = 0;
      dest[15] = 1;

      return dest;
    };

    /*
     * quat4.str
     * Returns a string representation of a quaternion
     *
     * Params:
     * quat - quat4 to represent as a string
     *
     * Returns:
     * string representation of quat
     */
    quat4.str = function(quat) {
      return "[" + quat[0] + ", " + quat[1] + ", " + quat[2] + ", " + quat[3] + "]";
    };

    return {
      vec3: vec3,
      mat3: mat3,
      mat4: mat4,
    };
  })()
);
